CN113313939A - Single lane cellular automata model simulation method considering acceleration continuity - Google Patents
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Abstract
The invention discloses a single lane cellular automaton model simulation method considering continuous acceleration, and provides a novel cellular automaton simulation model, which comprehensively considers the relationship between vehicle acceleration and the current speed, the maximum speed, the current speed and the front clearance of a vehicle on the basis of refining the length of road cells, refines the possible speed and acceleration of the vehicle, ensures that the acceleration does not jump in time, and realizes the single lane simulation model with continuous acceleration in the cellular automaton for the first time. The invention can solve the problem that the acceleration is not related or discontinuous with the last moment in the process of researching the vehicle updating by using the cellular automata model, and has important research value for simulating the road traffic flow by using the cellular automata model.
Description
Technical Field
The invention belongs to the technical field of traffic engineering, and particularly relates to a single lane cellular automaton model simulation method considering acceleration continuity.
Background
The cellular automaton has the characteristics of simply and efficiently simulating road traffic flow; however, the cellular automaton model discretizes space and time, so that the vehicle is always jumpy in the speed and position updating process, and the traffic flow characteristics of the vehicle when continuously changing cannot be well reflected. Researchers generally adopt a method of refining the road cellular space and the simulation step length to realize the optimization of the cellular automaton model; the acceleration of the vehicle in the cellular automaton is not optimized, the acceleration of the cellular automaton model is often set to be a fixed and unchangeable value, or whether the vehicle is accelerated selectively is judged according to the running space of the vehicle, and the acceleration of the vehicle in the next simulation step is unrelated to the acceleration of the vehicle in the previous simulation step; the acceleration of the vehicle at the next moment in the actual running process is changed on the basis of the acceleration at the moment; the acceleration of the vehicle is continuously changed in time, the jumping performance is not strong, and the existing cellular automaton model is different from the actual vehicle running acceleration in the acceleration of the vehicle.
Disclosure of Invention
The invention mainly aims to provide a single-lane cellular automata model simulation method considering continuous acceleration, which realizes control of the acceleration change of each space-time step vehicle in a cellular automata model, enables the simulation process of the cellular automata to be closer to the dynamic characteristic of vehicle running on an actual road, and overcomes the defects of speed jump and discontinuous acceleration of the existing cellular automata model.
In order to achieve the purpose, the invention adopts the technical scheme that:
a single lane cellular automata model simulation method considering acceleration continuity comprises the following steps:
s1, acquiring the current speed, the acceleration, the distance to the front vehicle and the speed of the front vehicle of the vehicle;
obtaining the current speed V, the acceleration a and the distance d between the current speed V and the acceleration a of the vehicle and the front vehiclenAnd front vehicle speed VfFor determining the safe distance d between two vehiclessafeAnd a first phase acceleration of the vehicle;
when the vehicle is an intelligent internet vehicle, the position, the speed and the acceleration of the vehicle can be known in the internet environment.
S2, judging whether the vehicle is accelerated or not;
the safe vehicle distance is the safe distance that the vehicle keeps to avoid a collision, and can be expressed as: when the vehicle suddenly experiences the maximum braking acceleration dmaxBraking, namely braking the vehicle at the current speed and acceleration until the two vehicles stop moving, wherein the difference between the running distance of the vehicle and the running distance of the front vehicle is obtained; if d isnGreater than dsafeThe vehicle can run at an accelerated speed because the vehicle does not collide with the preceding vehicle at the current speed and the accelerated speed, so that the vehicle enters an accelerated state;
s3, determining the stage-I virtual acceleration;
the current speed of the vehicle and the distance d from the vehiclenFront vehicle speed and vehicle maximum speed VmaxCalculating to obtain a stage-virtual acceleration a1,virtual；
S4, determining the acceleration of the first stage;
the stage one virtual acceleration is the maximum acceleration which can be reached by the vehicle under the conditions of the current speed and the current position; however, the acceleration of the vehicle does not change significantly from the previous moment, so that the virtual acceleration is limited; ensuring that the stage-one acceleration a is obtained within the acceleration change interval delta a1＝a+min(Δa,a1,virtual)；
S5, updating the cellular automaton deceleration step;
in the cellular automaton model after deceleration, a speed limiting rule set for avoiding vehicle collision restricts the maximum speed of the vehicle to be the current distance, and the dynamic characteristics of the motion of the vehicle cannot be expressed, so the step of updating the vehicle is not requiredVehicle acceleration; the vehicle speed after deceleration is V', and is calculated as V ═ min (V + a)1,dn)；
S6, judging whether the vehicle is randomly slowed or not;
the vehicle can randomly perform deceleration behavior in the driving process due to the random or frustrated psychology of a driver, the deceleration behavior is generated spontaneously by the vehicle, and therefore the acceleration in the slowing deceleration process needs to be considered in the acceleration of the vehicle; by generating a random number rand of zero to one1And the random moderation probability pslowdownComparing, and slowing down the vehicle if the random number is less than or equal to the random slowing down probability;
s7, calculating the virtual acceleration of the random slowing stage;
the random slowing is a deceleration phenomenon caused by psychological reasons of a driver, so that the deceleration phenomenon has randomness not only in time and space, but also in the acceleration of vehicle slowing; by generating a random number rand of zero to one2With the maximum random moderated acceleration d of the vehicleslowdown,maxDetermines the virtual acceleration a of the slowing-down phase2,virtualI.e. a2,virtual＝dslowdown,max×rand2；
S8, determining the acceleration of the second stage;
obtaining a virtual acceleration a2,virtualThen, considering that the acceleration of the vehicle does not change significantly with the last moment, the magnitude of the obtained virtual acceleration is limited, the acceleration is ensured to be continuous, and the final acceleration a in the second stage is obtained2(ii) a Ensuring that the final acceleration a of the stage two is obtained within the acceleration change interval delta a2＝a1+min(Δa,a2,virtual)；
S9, calculating the final speed and acceleration of the current vehicle;
from a phase two acceleration a2Obtaining the final acceleration a'; obtaining the final speed V 'of the current vehicle from the vehicle speed V' and the final acceleration a 'after the deceleration step of the cellular automaton model, wherein the final acceleration a' is a2The final speed V ═ V '+ a';
s10, updating the position;
obtaining the updated vehicle position from the initial vehicle position x and the vehicle final speed V', wherein the model adopts a periodic boundary condition, namely if one vehicle is driven out from the right boundary, the corresponding position of the left boundary is driven in by the same vehicle, so that the conservation of the number of the vehicles on the road is ensured; the conservation of the number of vehicles on the road is ensured; the vehicle initial position is x, and the updated vehicle position x' is x + V ".
Specifically, the step S2 is to determine whether the vehicle is accelerating, specifically:
calculating the safe distance from the current speed, acceleration, front speed and maximum deceleration of the vehicle, if dnGreater than dsafeThe vehicle is in an acceleration state because the vehicle does not collide with the front vehicle at the current speed and acceleration; let the current speed be V, the acceleration be a and the speed of the front vehicle be VfMaximum braking acceleration d of the vehicle and the preceding vehiclen,max，dn+1,max(ii) a The safe vehicle distance calculating step comprises the following steps:
s21, calculating the time T between braking and stopping of the vehicle, namely (V + a)/dn,max(ii) a Time T from braking to stopping of front vehiclef＝Vf/dn+1,max；
S22, calculating the braking distance of the vehicle
Braking distance of front vehicle
Obtaining a safety distance dsafe＝S-Sf；
S23, comparison dsafeAnd dnSize; when d isn>dsafeWhen the current vehicle is accelerating.
Specifically, the step S3 determines a stage-one virtual acceleration, specifically,
stage-one virtual acceleration a1,virtualThe linear functions are defined as the current speed influence factor alpha of the vehicle, the speed difference influence factor beta of the vehicle and the front vehicle and the clearance influence factor gamma of the vehicle and the front vehicle; the speed of alpha, beta and gamma to the current speed of the vehicle, the speed difference between the vehicle and the front vehicle and the vehiclePositive correlation with the front car gap and the maximum acceleration a of the vehiclen,maxNegative correlation, an,maxObtained by converting real vehicle dynamics parameters; the phase-one virtual acceleration calculation process is that,
1) the current speed influence factor alpha k of the vehicleα(Vn,max-V)/Vn,max(ii) a Influence factor beta of speed difference between the vehicle and the front vehicle is kβ(Vf-V)/Vn,max(ii) a Influence factor gamma k between the vehicle and the front vehicleγmin(dn,Vn,max)/Vn,max(ii) a Wherein k isα、kβ、kγThe weight of the three influence factors is satisfied with kα+kβ+kγ＝1；Vn,maxThe maximum speed of the vehicle is obtained by converting the maximum speed of the real vehicle;
2) calculating to obtain a stage-virtual acceleration a1,virtual＝amax(kαα+kββ+kγγ)。
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a new cellular automaton simulation model, which comprehensively considers the relation between the vehicle acceleration and the current speed, the maximum speed, the current speed and the front clearance of the vehicle on the basis of refining the road cell length, refines the possible speed and acceleration of the vehicle, ensures that the acceleration does not jump in time, and realizes the acceleration continuous single lane simulation model in the cellular automaton for the first time.
The invention can solve the problem that the acceleration is not related or discontinuous with the last moment in the process of researching the vehicle updating by using the cellular automata model, and has important research value for simulating the road traffic flow by using the cellular automata model.
Drawings
FIG. 1 is a flow chart of the model of the present invention;
FIG. 2 is a graph of density versus flow for an embodiment of the present invention and a standard NS model
FIG. 3 is a graph of density versus velocity for an embodiment of the present invention and a standard NS model
FIG. 4 is a graph of density versus acceleration for an embodiment of the present invention and a standard NS model
FIG. 5 is a scatter plot of acceleration versus time for density according to the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings.
The effect evaluation is carried out on the simulation model of the single-lane cellular automata considering the acceleration continuity by an example.
Taking the length of each cell as 1m, the length of a vehicle as 6m, and corresponding to 6 cells; the simulated vehicles have the same dynamic parameters; the maximum speed of the vehicle is 30m/s, and the maximum acceleration is 5m/s2Maximum braking acceleration of-6 m/s2The random moderated maximum acceleration is-3 m/s2The random slowing-down probability is 0.3, and the allowable variation acceleration range delta a is +/-2 m/s2，kα＝0.2,kβ＝0.3,kγ0.5; the length of the simulation road section is 1200m, as the simulation is a periodic boundary condition, the density putting interval delta rho is set to 1/1000pcu/h, one thousand data points are total, the simulation time is 5000s, the 1000s data are taken as result analysis data, the simulation coding software is Matlab, and the characteristic curve shown in the attached figures 2-5 is obtained.
As can be seen from the flow density relationship diagrams and the density-speed diagrams of fig. 2 and 3, when the traffic density is about 0.14pcu/km and the traffic flow approaches the maximum value, the traffic flow of the cellular automaton model with continuous acceleration is considered to suddenly drop, which is in accordance with the traffic flow failure phenomenon in the traffic flow phenomenon; meanwhile, it can be found from the figure that when the traffic density is 0.12-0.17 pcu/km, the flow density graph has upper and lower branches, when the initial vehicle throwing position is set well, the upper half branch is obtained, and when the throwing position is poor, the lower half branch is obtained, which accords with the hysteresis phenomenon in the traffic flow; when the NS model is analyzed, we can also obtain the above traffic flow phenomenon, but the displayed effect is not as good as the cellular automaton model considering the acceleration continuation.
Meanwhile, as can be seen from fig. 2, in the right half part of the density flow chart, data points do not appear to be one-dimensional linear as in the left half part, and the data points in the right half part are dispersed in a two-dimensional area, so that the wide motion blockage part in the three-phase traffic flow theory conforms to the actual traffic flow phenomenon; this is not apparent from the NS model; the maximum traffic capacity of the single-lane cellular automaton model with continuous acceleration is calculated to be 2160 pcu/h; the intersection point of the upper half part and the lower half part of the flow density graph is about 0.6pcu/s, the traffic capacity obtained by a conversion unit is 2160pcu/h, accords with the theoretical highway traffic capacity, can be used for actual highway traffic flow simulation, and the traffic capacity obtained by the calculation of the NS model is about 2448pcu/h, has large difference with the theoretical traffic capacity and has large simulation error.
FIG. 4 shows the relationship between the classical NS model and the acceleration of the model of the single-lane cellular automata considering the acceleration continuity as a function of the density. In the actual driving process of the vehicle, as the current road density is continuously increased, the gap between the vehicles is also reduced, and the acceleration desire of the vehicle is continuously reduced. FIG. 3 shows that the acceleration as a whole is reduced with the density; as for the jumping phenomenon of the traffic flow acceleration at the density of about 0.15pcu/km, because the density is in a metastable state region, if the initial vehicle throwing setting is better, the vehicle can have better driving environment, and the upper half part of the acceleration can be obtained; if the initial throwing position is set to be poor, the vehicle begins to deform into a blockage, and the lower half part of the acceleration is obtained, which corresponds to the traffic flow hysteresis; however, in the NS model, since the acceleration of the vehicle is not related to the acceleration at the previous time and the magnitude of the acceleration is related to only the fixed slowing probability, the acceleration is substantially constant, which is not practical, and therefore, it is very suitable to study the traffic flow using the present model.
Fig. 5 shows the acceleration of the vehicle over time for different densities. It can be seen that although the acceleration still has a volatility in time, the change in acceleration per second is limited to a range of Δ a due to the constraints on the change in acceleration herein, satisfying the acceleration continuation assumption highlighted by the present invention.
Claims (3)
1. A single lane cellular automata model simulation method considering acceleration continuity is characterized by comprising the following steps:
s1, acquiring the current speed, the acceleration, the distance to the front vehicle and the speed of the front vehicle of the vehicle;
obtaining the current speed V, the acceleration a and the distance d between the current speed V and the acceleration a of the vehicle and the front vehiclenAnd front vehicle speed VfFor determining the safe distance d between two vehiclessafeAnd a first phase acceleration of the vehicle;
s2, judging whether the vehicle is accelerated or not;
safety distance dsafeThe safe distance for the vehicle to maintain to avoid a collision can be expressed as: when the vehicle suddenly experiences the maximum braking acceleration dmaxBraking, namely braking the vehicle at the current speed and acceleration until the two vehicles stop moving, wherein the difference between the running distance of the vehicle and the running distance of the front vehicle is obtained; if d isnGreater than dsafeThe vehicle can run at an accelerated speed because the vehicle does not collide with the preceding vehicle at the current speed and the accelerated speed, so that the vehicle enters an accelerated state;
s3, determining the stage-I virtual acceleration;
the current speed of the vehicle and the distance d from the vehiclenFront vehicle speed and vehicle maximum speed VmaxCalculating to obtain a stage-virtual acceleration a1,virtual；
S4, determining the acceleration of the first stage;
the stage one virtual acceleration is the maximum acceleration which can be reached by the vehicle under the conditions of the current speed and the current position; considering that the acceleration of the vehicle does not change significantly with the last moment, the size of the obtained virtual acceleration is limited; ensuring that the stage-one acceleration a is obtained within the acceleration change interval delta a1＝a+min(Δa,a1,virtual)；
S5, updating the cellular automaton deceleration step;
the vehicle speed after deceleration is V', and is calculated as V ═ min (V + a)1,dn)；
S6, judging whether the vehicle is randomly slowed or not;
taking into account the acceleration of the slowing-down process into the vehicle acceleration by generating a zero-to-one randomNumber rand1And the random moderation probability pslowdownComparing, and slowing down the vehicle if the random number is less than or equal to the random slowing down probability;
s7, calculating the virtual acceleration of the random slowing stage;
by generating a random number rand of zero to one2With the maximum random moderated acceleration d of the vehicleslowdown,maxDetermines the virtual acceleration a of the slowing-down phase2,virtualI.e. a2,virtual＝dslowdown,max×rand2；
S8, determining the acceleration of the second stage;
obtaining a virtual acceleration a2,virtualThen, considering that the acceleration of the vehicle does not change significantly with the last moment, the magnitude of the obtained virtual acceleration is limited, the acceleration is ensured to be continuous, and the final acceleration a in the second stage is obtained2(ii) a Ensuring that the final acceleration a of the stage two is obtained within the acceleration change interval delta a2＝a1+min(Δa,a2,virtual)；
S9, calculating the final speed and acceleration of the current vehicle;
from a phase two acceleration a2Obtaining the final acceleration a'; obtaining the final speed V 'of the current vehicle from the vehicle speed V' and the final acceleration a 'after the deceleration step of the cellular automaton model, wherein the final acceleration a' is a2The final speed V ═ V '+ a';
s10, updating the position;
the vehicle initial position is x, and the updated vehicle position x' is x + V ".
2. The method for simulating the cellular automaton model of the single lane considering the acceleration continuity, according to claim 1, wherein: step S2 is to determine whether the vehicle is accelerating, specifically:
calculating the safe distance from the current speed, acceleration, front speed and maximum deceleration of the vehicle, if dnGreater than dsafeThe vehicle is in an acceleration state because the vehicle does not collide with the front vehicle at the current speed and acceleration; let the current speed be V, the acceleration be a and the speed of the front vehicle be VfMaximum braking acceleration d of the vehicle and the preceding vehiclen,max，dn+1,max(ii) a The safe vehicle distance calculating step comprises the following steps:
s21, calculating the time T between braking and stopping of the vehicle, namely (V + a)/dn,max(ii) a Time T from braking to stopping of front vehiclef＝Vf/dn+1,max；
S22, calculating the braking distance of the vehicle
Braking distance of front vehicle
Obtaining a safety distance dsafe＝S-Sf；
S23, comparison dsafeAnd dnSize; when d isn>dsafeWhen the current vehicle is accelerating.
3. The method for simulating the cellular automaton model of the single lane considering the acceleration continuity, according to claim 1, wherein: the step S3 determines a stage-one virtual acceleration, specifically,
stage-one virtual acceleration a1,virtualThe linear functions are defined as the current speed influence factor alpha of the vehicle, the speed difference influence factor beta of the vehicle and the front vehicle and the clearance influence factor gamma of the vehicle and the front vehicle; alpha, beta and gamma are respectively positively correlated with the current speed of the vehicle, the speed difference between the vehicle and the front vehicle, the gap between the vehicle and the front vehicle and the maximum acceleration a of the vehiclen,maxNegative correlation, an,maxObtained by converting real vehicle dynamics parameters; the phase-one virtual acceleration calculation process is that,
1) the current speed influence factor alpha k of the vehicleα(Vn,max-V)/Vn,max(ii) a Influence factor beta of speed difference between the vehicle and the front vehicle is kβ(Vf-V)/Vn,max(ii) a Influence factor gamma k between the vehicle and the front vehicleγmin(dn,Vn,max)/Vn,max(ii) a Wherein k isα、kβ、kγIs weighted by three influence factorsHeavy, satisfy kα+kβ+kγ＝1；Vn,maxThe maximum speed of the vehicle is obtained by converting the maximum speed of the real vehicle;
2) calculating to obtain a stage-virtual acceleration a1,virtual＝amax(kαα+kββ+kγγ)。
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